Unit Plan 24 (Grade 5 Math): Classifying 2D Figures by Properties
5th graders classify 2D figures by properties like sides, angles, and parallel lines—using definitions, if–then reasoning, and hierarchy logic to prove and defend geometric classifications.
Focus: Use attributes (side lengths, angles, parallel/perpendicular lines) to classify two-dimensional figures; make and defend claims using definitions and property logic.
Grade Level: 5
Subject Area: Mathematics (Geometry)
Total Unit Duration: 5 sessions (one week), 45–60 minutes per session
I. Introduction
Students move beyond “looks like” sorting and classify quadrilaterals and other polygons by defining properties. They learn that when a figure belongs to a category, it also belongs to all of that category’s subcategories whose properties it meets (e.g., every square is also a rectangle and a parallelogram). The emphasis is on clear definitions, if–then reasoning, and justifying classifications.
Essential Questions
- Which properties determine a figure’s category, and which are just appearances?
- How do definitions help us sort and name shapes consistently?
- Why does membership in a subcategory imply membership in the broader category?
- How can I defend a classification with property statements (not pictures)?
II. Objectives and Standards
Learning Objectives — Students will be able to:
- Identify and use attributes (side lengths, parallel/perpendicular lines, angle types) to classify 2D figures.
- Apply definitions of common quadrilaterals (parallelogram, rectangle, rhombus, square, trapezoid) to determine category membership.
- Explain hierarchical relationships among categories (e.g., all squares are rectangles; all rectangles are parallelograms).
- Construct and critique arguments using precise vocabulary and if–then statements.
- Create sorting rules/diagrams that show how properties drive classifications.
Standards Alignment — CCSS Grade 5
- 5.G.3: Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category; classify figures in terms of properties.
- Mathematical Practices emphasized: MP.1 (persevere), MP.3 (justify/critique), MP.6 (precision), MP.7 (look for structure).
Success Criteria — Student Language
- I can name the properties that define a category (not just what it looks like).
- I can use if–then statements to show why a figure fits a category.
- I can explain why a square is also a rectangle and a parallelogram.
- I can build a sorting diagram that organizes figures by their attributes.